Food waste and stockouts are widely recognized as an important global challenge. While inventory management aims to address these challenges, the tools available to inventory managers are often limited and the usefulness of their decisions is dependent on demand realizations, which are not within their control. Recommender systems (RS) can influence and direct customer demand, e.g., by sending personalized emails with promotions for diferent items. We propose a novel approach that combines the opportunities provided by RS with inventory management considerations. Under the assumption that there is a known set of customers to receive a promotion consisting of items, we use mixed-integer programming (MIP) to allocate recommended items across customers taking both individual preferences and the current state of inventory with uncertainties into account. Our approach can solve problems with both stochastic supply (inventory and perishability) and demand. We propose heuristics to improve scalability and compare their performance with the optimal solution using data from an online grocery retailer. The goal is to target the right set of customers who are likely to purchase an item, while simultaneously considering which items are prone to expire or be out-of-stock soon. We show that creating recommendation lists exclusively considering user preferences can be counterproductive to users due to possible excessive stockouts. Similarly, focusing only on the retailer can be counterproductive to retailer sales due to the number of expired products that can be considered lost income. We thus avoid the loss of customer goodwill due to stockouts and reduce waste by selling inventory before it expires. CCS Concepts: • Information systems → Personalization; Recommender systems. Additional Key Words and Phrases: Recommender systems, mixed-integer programming, perishability, multi-objective optimization
With about one-third of food lost or wasted, avoiding food waste has become a global challenge due to its environmental
and economic impact [
Retail food waste occurs when supply exceeds demand. A simple solution is for retailers to order less and thus
decrease supply. This, however, increases the number of stockouts and consequently reduces customer goodwill [
Although the decision maker has a notion of what to expect in the future, customer demand and whether they would
buy a recommended item is not deterministic. Consequently, inventory levels are also stochastic since the decision
∗Copyright 2022 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
Presented at the MORS workshop held in conjunction with the 16th ACM Conference on Recommender Systems (RecSys), 2022, in Seattle, USA.
maker does not know in advance how much demand will occur on a specific day and how much stock will be left at the
end of the day. Additionally, inventory levels might not be recorded correctly, or a set of items might arrive sooner or
later than expected, causing the inventory to fluctuate unexpectedly. Some soon-to-perish items might go bad sooner
or later than expected according to the storage conditions and the type of item [
In the RS literature, earlier works mostly focused solely on user preferences. More recent works started incorporating
the needs of the item providers, the RS platform/system itself, and other stakeholders. Multistakeholder recommender
systems (MRS) are introduced as systems that include the objectives of parties other than the users. These objectives
may conflict with each other, and solutions recommended by MRS algorithms take all these objectives into account
while creating the recommendation lists that consist of items ofered to the users [
Given the proliferation of digital shopping environments such as websites and mobile shopping apps where many
user behaviors can be recorded, more data is available to tailor promotions to the needs of individual users [
We contribute to the RS literature by proposing and solving a mixed-integer-programming (MIP) model that combines RS and inventory management. Our proposed model creates recommendation lists that consider both user and retailer perspectives, as well as the system-enforced perishability and stockout concerns. Additionally, our model accounts for the stochastic nature of perishables, demands, and inventory levels. By including stochasticity and considerations of the users, the retailer, and the system, we discuss the complex economical impacts of RS in an online retailer setting. As far as we know, our approach to this online retailing problem and our optimization model are novel additions to the RS literature. Furthermore, using ideas from our optimization model, we propose heuristics that improve scalability eficiently. Finally, we discuss the results of our optimization model and heuristics and show that our approaches ofer solutions that improve user, retailer, and system objectives simultaneously.
This section surveys relevant literature from sales promotion, RS, and inventory management. There is extensive research in the sales promotion literature showing the efectiveness of email promotions, and RS articles have already investigated the efects of personalization in driving retail sales. Likewise, there is research in the inventory management literature showing the importance of alleviating the stockout and perishability issues, mostly focusing on the retailer. Our contribution is to combine these approaches to create personalized email promotions that consider both the user’s preferences as well as retailer and supply chain objectives to avoid perishables and stockouts.
Sales promotion is a widely used strategy defined as an “action-oriented marketing event whose purpose is to have
a direct impact on the behavior of the firm’s customers” [ 42, p. xvii]. Promotions include price discounts, feature
advertising, and other touch points such as targeted emails, special displays, and coupons. Promotions stimulate market
demand, enable retailers to sell excess items, and increase their revenue. There is a long literature studying sales
promotions and their efects [
Others have used RS to implement personalized shopping lists. Lin et al. [
Perishable items and limited inventory appear in multiple works in the dynamic assortment and inventory control
literature, but without considering how promotions can be used to manage them. Bernstein et al. [
This section proposes a MIP model and a heuristic to solve an item recommendation problem considering both retailer and user perspectives. We maximize both the quality of the recommendations for the users and the impact on the retailer’s profitability (perishability, sales). For this purpose, we first discuss the problem definition and assumptions. We then illustrate and explain our optimization model and heuristic. 3.1
We consider an online retailer selling physical items to their users over the internet. The retailer periodically creates a personalized top- promotion list such as a weekly email recommending items ( ) to a known set of users ( ); hereafter we use the RS term user instead of retailing terms customer or consumer. Therefore, we solve the problem of selecting which items should be recommended to the users in the form of personalized email promotions. While creating top- lists is a common RS task, we allow lists with fewer than items to accommodate situations with very low inventory levels; hereafter we use the term “top- list” with the understanding that some lists may have fewer than items. We assume that recommending item to user might result in a demand increase for the said item. Note that the RS can increase demand without reducing the price and thus profit margin. We assume that the retailer’s purchase cost of item is , and that the retailer earns profit × when it sells the item, where is the markup and = (1 + ) × is the revenue (selling price). We allow for items to have diferent prices but assume a constant markup (this assumption can be easily relaxed).
When deciding which items should be recommended, the following four aspects are considered. Firstly, since the
available in-stock inventory () is limited, there is a possibility of stockouts if users are unable to buy items due to
unavailability. When users attempt to purchase a recommended item that is out of stock, we assume that the retailer
incurs a penalty of , which measures a loss of goodwill and revenue from the sale. Secondly, some items are perishable
with quantity considered soon-to-perish (0 ≤ ≤ , ∀ ∈ ). Soon-to-perish items must be sold as soon as possible;
otherwise, they will be discarded since the retailer cannot sell expired items. For any discarded item, the retailer incurs
a penalty (i.e., there is no cost to dispose of the perished items nor salvage value). We also assume that items are
shipped following the FIFO (first-in-first-out) method, where items that expire the soonest are shipped first. Retailers
enforce FIFO by keeping longer-lasting items in storage. FIFO is often used in the literature with perishable items [
We consider these four aspects from either the user’s or retailer’s perspective. We create these perspectives by including system-enforced sustainability and stockout considerations to the traditional user consideration of utility/rating and retailer consideration of revenue. From the user’s perspective, the recommended list should have items with a high average rating, while avoiding stockouts. The retailer wants to stimulate demand for items that generate high profit, while also avoiding items to perish. Balancing between these perspectives is crucial. The retailer may, for example, need to recommend items with a lower user rating to avoid items perishing. The retailer thus determines the recommendation lists considering the number of perishable items, demand, inventory, and possible demand increase after recommendations. If these values are known with certainty, the problem is deterministic. In this case, after ifnalizing all recommendation lists, the decision maker knows exactly how many items will be sold, what the profits will be, the average user rating, the numbers of stockout and perished items, and their costs. However, in practice, the decision maker rarely has access to complete information.
By considering stochasticity in our model we obtain top- lists that account for unexpected situations. Therefore, we
incorporate uncertainties in inventory () and soon-to-perish items ( ) (both vectors of length | |), and demands with
| | × | | matrix . For example, if each value in , , were binary then there would be a total of 22| |+| | | | scenarios
to investigate. Even with only two realizations, an exhaustive enumeration would be intractable. One solution to this
problem is to use Monte Carlo sampling to obtain a finite number of scenarios and the Sample Average Approximation
(SAA) method to solve them [
max ,,, ∈ ≤ (∀ ∈ , ∈ []) ≥ − (∀ ∈ , ∈ []) + = ∑︁ + (∀ ∈ , ∈ [])
∈
, , ≥ 0, ∈ {0, 1} (∀ ∈ , ∈ , ∈ [])
ˆ / −
∑︁
Equation (1) specifies our multi-objective function that considers both the user and retailer perspectives. Inside the left
parenthesis, we maximize the average estimated ratings and minimize the cost incurred when a demanded item is out
of stock (stockout). Inside the right parenthesis, we maximize the revenue of the retailer from the sales and minimize
the cost incurred from the perished items. We divide the estimated ratings by to lower the efect of choice of on the
solution quality. Trade-of parameter ∈ [
Since we assume FIFO we can preprocess some of the uncertainties. For each scenario and item , we update
= max 0, − Í∈ and = max 0, − Í∈ . These are the respective counts of inventory ( ) and
soon-to-perish items ( ) when the RS is not applied (we only consider initial demands). Next, suppose that we
wso1irt≤thth˜12e =≤nu·m1·,b·ae≤nrdo,f−˜p1e≤r=isha.+bT1leh−einte, mw,s∀e(cr∈e)aa{tne1,dt.w.i no.,viennc−rteo1mr}yewn(itta)hlains˜cfro=elalosew a.srDrfoaeyrfinseefaocrhea=,ch1Í∈:≤˜(=2 ≤× −··)·,−≤w1,h∀ic−h1∈r≤e{p2,re..s,.ea,nntd}s
the expected demand increase for item after implementing the RS. Next, we apply the remodeling idea suggested by
Ferguson and Dantzig [
(∀ ∈ ) =1 ˜ , ˜ ≥ 0, ∈ {0, 1} (∀ ∈ , ∈ , ∈ []) Equation (7) is a reformulation of equation (1) with new decision variables. For item , ˜ is the number of soon-to-perish items sold and ˜ is the number of stockouts in scenarios. Then, for calculating the perished items we use the coeficient ( + 1 − ) and penalize (˜ − ˜ ). or calculating the stockouts we use the coeficient and penalize ˜ . Note that we use incremental increase arrays (˜, ˜) in this step. Because of how is defined, every recommendation increases the equation (7) by . The additional term Í ˜ removes this increase if item stockouts. Constraint (8) ∈ remains the same as constraint (2). Constraints (9) and (10) are simple bounds on decision variables ˜ and ˜, which are cannot exceed generally easily handled by commercial optimization software. Constraint (11) enforces that sum of ˜ should be greater than or equal to − 1. Constraint (13) remains the same . Constraint (12) enforces that sum of ˜ as constraint (6), except in this model, decision variable is removed. The value of ˜ is 0 if = −1 (same with ). Then, the corresponding decision variable ˜ (˜ ) is removed since it is fixed to 0. These changes improve the previous optimization model’s computational time and memory requirement. 3.2
For very large datasets, optimization models can struggle with large memory requirements and slow solution times. We ofer a heuristic that scales better for larger datasets. This heuristic is both easy to implement and fast to run. We first randomize the order of users. In each step, we recommend a single item to user , and then move on to the next user. This procedure continues until either all users have items in their lists or adding an item to a user’s list decreases the objective function value, which only happens if all the inventory is depleted. For a given user , we recommend the item ∗ that solves the objective function: ∗ = argmax 1 ∑︁ (ˆ / − min(0, − )) + (1 − ) ( min( , ) + min( , )).
∈ =1 (14) After each recommendation, the , and recommendation lists of users are updated: ∗ = max(0, ∗ − ∗ ), and ∗ = max(0, ∗ − ∗ ). Each item ∗ recommended to user has rating ˆ∗ /. The value of ∗ is the demand increase of item ∗ for user . If the term ∗ − ∗ is negative, recommending item ∗ to user causes a stockout having penalty ∗ . When a soon-to-perish item ∗ is recommended to user , we incentivize that recommendation by the cost of the item (∗ ) times the number of soon-to-perish items sold (min{∗, ∗ }). Lastly, when the retailer sells an item, the objective value increases by × . The heuristic requires solving objective function (14) at most | | times. 3.3
Our optimization model can be solved optimally for hundreds of scenarios and thousands of users and items. However,
in cases with thousands of scenarios and millions of users and items, we need approximation methods to obtain a
solution in a reasonable length of time. This subsection discusses two approximation approaches. First, co-clustering
[
Second, we apply a simple idea that we call the “best- approach,” in which we recommend item to user only if
either item is one of the top rated items by that user , or user is one of the top users that rated that item the
highest. None of the other user-item pairs will be considered for recommendation. The decision maker can choose
by using a grid-search algorithm. A similar approach was implemented in the RS literature [
This section discusses the data used in our paper and the computational results of the models proposed. All results are
obtained by using a laptop with Intel(R) Core(TM) i7-8750H CPU @ 2.20GHz 2.21 GHz processor information with
16.0 GB of installed RAM specifications. The optimization model is solved using Gurobi, a commercially available
mathematical programming solver, [
We consider an online grocery retailer located in the United States and learn user preferences from their purchase
history. We examine regular users who have shopped at least 15 times within the last 6 months, giving 3731 users (| |)
with 78,195 orders. These orders include 27,158 unique item stock-keeping units (SKUs). Each SKU has a price, brand,
and category from a retailer-provided taxonomy. We aggregate the SKUs following [
Average demand values are calculated by averaging the quantity bought for each user-item pair for a week, denoted
as . We create a | | × | | rating matrix by using the function log( + 1), as the number of orders including item ∈
for user ∈ . Next, we compare prediction algorithms SVD, -NN, and Co-clustering using the Surprise package [
Manuscript submitted to ACM 4.2
This subsection discusses the settings and metrics used to evaluate our models, and benchmarks implemented to compare our approaches. These benchmarks are denoted , , , and , and they solely optimize perishability, retailer sales, stockouts, and average user rating objective functions, respectively. In other words, each benchmark obtains a solution considering only one criterion. Therefore, we compare our solutions solving multiple objectives with those focusing on a singular objective. The letter indicates the heuristic solution and indicates optimization. This letter is followed by a number indicating the weight () value. For example, the optimization solution with weight = 0.5 is denoted as 5. We obtain solutions for ∈ {0.1, 0.5, 0.9}, corresponding to a higher focus on retailer perspective, equal focus, and a higher focus on user perspective, respectively.
We investigate four settings: high perishables and low stockout risk (HL), low perishables and high stockout risk
(LH), both high risk (HH), and finally, both low risk (LL) settings. Settings with a high risk of perishables have a larger
number of soon-to-perish items , and those with a high risk of stockout have lower levels of inventories . We choose
= {0.2, 0.6} and = {30, 100}, and their combinations create our four settings. We generate inventory levels using
∼ Poisson( + Í ), where is the expected demand for item and user . Average demands vary greatly
from as low as 0.4t∈oas much as thousands. We choose lower values for high-risk stockouts and higher values
otherwise. The demand values are distributed as Poisson( ). In this way, we create upper bounds that are tight
relative to the total demand of each item. We create a number of soon-to-perish items as a percentage of inventories
such as = , where is distributed as a truncated normal N (, 0.1) with bounds [
Unless stated otherwise, we generate 500 scenarios () for , , and considering each of the four settings. We obtain solutions for each approach by solving the problem with these 500 scenarios. Then, we generate 2500 new out-of-sample scenarios to test the quality of the obtained solutions. Overall, a solution is better if it has higher user ratings, retailer sales, or lower perishability and stockout objective values. These objective values (metrics) are calculated as follows, where x is 1 if item is recommended to user and 0 otherwise, s is the number of item sold, z is the number of perished item , y is the number of stockouts of item :
Ratings = ∑∈︁ ∑∈︁ ˆ x, Sales = ∑∈︁ s, User Perspective = Ratings − Stockouts,
Perishability = ∑︁ z,
Stockouts = ∑︁ y, ∈ Retailer Perspective = Sales − Perishability This subsection presents and discusses results obtained using our optimization model and heuristics, and compares them with solutions of benchmark models. Furthermore, we investigate the efect of including stochasticity and heuristics on the solution quality. HH
HL
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(b) Retailer perspective objective values HH
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LL 4.3.1 Solution Quality of Optimization Approach. We compare our model’s solution with the benchmarks in Figure 1. We use the best- method with = 100 and ofer at most = 10 items to every user. Figure 1 (a) shows that the overall objective values for the user perspective, which includes user ratings and stockouts, are similar for all approaches, except for , which is the benchmark where only the average user rating is optimized. Despite performing well in terms of user rating (Figure 1 (c)), users would experience many stockouts (Figure 1 (e)) that reduce customer goodwill, which results in significantly worse user perspective objective value. As expected, in the high stockout risk settings (HH and LH) the number of stockouts observed is greater, causing slightly lower user perspective objective values. The optimal approach achieves the highest user perspective objective values for all settings.
Considering the objective values from the retailer perspective, which include perished items and sales, we observe more varied results than those from the user perspective. The values for the high perishables and low stockouts (HL) are the lowest, indicating that many items perish, which generates high waste costs, as illustrated by Figure 1 (f). The exact opposite setting with low perish and high stockout (LH) achieves the highest retailer perspective values because of the low waste costs. The retailer perspective objective values are similar for HH and LL, which is surprising at first because they consider exact opposite situations. Looking into these results in more detail, we see that for LL, the sales are higher than for HH (Figure 1 (d)), but so are the number of perished items. In general, the solutions tend to slightly decrease the sales objective values to improve the perishability objective, resulting in a better retailer perspective objective value. We next discuss each individual objective in more detail.
When considering the user ratings in subfigure (c), performs the best, but as discussed before, sufers from a
high number of stockouts (Figure 1 (e)), which negatively afects users. Interestingly, the solution results in high user
ratings as well but incurs higher stockouts too. The solution ofers items with the greatest monetary gain considering
the users’ probability of buying the item recommended to them. This can also be observed from subfigure (d), where
achieves the highest sales objective values. This benchmark is diferent from only ofering items with high price margins,
and additionally considers the probability of users buying the recommended item, thus achieving recommendations
with high user ratings. Therefore, this competitive benchmark considers both retailer and user information, and is
most similar to approaches that maximize the retailer’s expected profit [
Subfigure (d) shows the sales objective function values. The LL setting results in the greatest sales due to the retailer being able to sell the highest profit items in a low-risk stockout and perishability environment. Counterintuitively, most of the time sales increase when the optimization solution focuses less on the retailer perspective. This happens because an increased focus on the retailer perspective usually lowers the current sales in favor of selling lower-margin and lower-rating items that will perish soon, causing long-term profits instead of short-term. Generally, less focus on retailer perspective results in less focus on recommending soon-to-perish items, thus increasing the retailer sales but decreasing the retailer perspective objective value due to perished items. This is again an important distinction that traditional RS might miss while trying to maximize the revenue of the retailer. However, the LH setting is an exception to this rule. The optimization solutions in setting LH already have a low number of perished items (subfigure (f)) and thus a weight increase results in recommending high-rating items that are not necessarily high profit for the retailer while lowering the stockouts. Benchmarks and perform the worst because sales are negatively afected when the only concern is selling soon-to-perish items or keeping the stockouts to a minimum.
The number of stockouts (see Figure 1(e)) is in a similar range for all approaches except for benchmark . Interestingly, the approach might seem to be user-centric, however, it results in a poor user experience because Manuscript submitted to ACM of the large number of stockouts, where users cannot purchase items that were recommended to them. This is an important and general shortcoming of the top- recommendation rule and is a disadvantage of applying RS without considering demand changes that follow. Our optimization solution considers user experience overall and results in users obtaining the items that are recommended to them. Next, benchmark solely focuses on minimizing the stockout objective function. In this benchmark, not recommending anything is one solution with the optimal value of 0. This benchmark is useful for analyzing the solution quality when little to no recommendations are made. The objective values of perishability, user ratings, and sales are significantly underperforming. Interestingly, due to the existence of multiple-optima solutions, the sales objective value is not exactly zero in some cases. For the optimal solutions, larger weights result in better stockout objective values because the focus shifts to the user perspective.
Figure 1 (f) shows the perishability objective function values. HL has the highest perishability values due to high inventory (low stockout risk) and high-risk perishability, which results in the greatest number of soon-to-perish items. We observe that low stockout with a low perishability ratio (LL) can result in a larger number of perished items than low inventory with a high perishability ratio (HH). Thus, we note that low risk stockout is not always desirable and the retailer should order less to reduce the number of perished items due to high inventory levels. The benchmark minimizes the perishability objective function by recommending soon-to-perish items first, and thus achieves the best perishability results. The optimization solution with weight 0.1 is a close second to in the perishability objective. However, benchmark struggles when it comes to sales and user ratings. The proposed recommendations are neither what users prefer nor the items with high-profit margins. If the RS focuses solely on soon-to-perish items, both retailer and user perspectives sufer. The perishability objective, in general, decreases when the weight decreases due to more focus on the retailer perspective.
Overall, considering the user and retailer perspectives in subfigures (a) and (b), the benchmark performs badly on the user metrics due to stockouts, and performs badly on retailer metrics due to low sales. Benchmark performs worse in user perspective when stockout is high risk, and in retailer perspective when perishability is high risk. Benchmark might seem like a good option for the retailer at first, however, the stockouts and perished items that are ignored make it undesirable. Benchmark performs worse than our models on user ratings and sales, due to recommendations being made towards selling the soon-to-perish items without considering user ratings or revenue. We have investigated two additional benchmarks: user-perspective (consider both user rating and stockouts) and retailer-perspective (consider both retailer sales and perishability). The user-perspective benchmark was only slightly better in user perspective objective value while significantly worse in retailer perspective objective value relative to the optimization solution due to a high number of perished items. The retailer-perspective objective value was almost identical to the optimization solution but significantly worse in user perspective solution due to a high number of stockouts. Overall, the optimization solutions perform the best when considering both the user and retailer perspectives. 4.3.2 Solution Quality of Heuristic Approach. Figure 2 compares the objective function values for heuristic approaches. Each subfigure considers one of the four settings with best- approach applied, where ∈ {100, 500}. The diference in the objective values between = 100 and 500 is minimal. The objective function value diference is even smaller for > 500. This result is very useful for a retailer ofering a large number of products since only considering a smaller subset of the most preferred products for each user and most preferred users for each product decreases the problem size significantly. Therefore, using the best- approach improves the memory and solution time for both models while maintaining the solution quality. We note that our heuristic approach also achieves objective function values close leu170 a V e150 v i t c je130 b O 110 175 e u la150 V e iv125 t c e jb100 O 75 250 e u l a V200 e v i t c jeb150 O e lu200 a V e v i tc100 e j b
O
H1H5H9O1O5O9H1H5H9O1O5O9 H1H5H9O1O5O9H1H5H9O1O5O9 H1H5H9O1O5O9H1H5H9O1O5O9 H1H5H9O1O5O9H1H5H9O1O5O9 (a) = 0.2 and = 100 (Seting (b) = 0.2 and = 30 (Seting (c) = 0.6 and = 100 (Seting (d) = 0.6 and = 30 (Seting LL) LH) HL) HH) to the optimal solution (within 1%). The heuristic performs similarly to the optimization model that considers all the metrics in Equation 15. 4.3.3 Solution Quality Comparison of Stochastic and Deterministic Cases. We analyze the solutions using expected values of , , instead of creating 500 scenarios for demand, inventory, and perishability. We denote these solutions with and use the same weights as before, i.e., {0.1, 0.5, 0.9}. Figure 3 shows that it is advantageous to consider stochasticity because using only the expected values ignores the variance of the data. We conclude that it is better to account for uncertainty compared to using a solution estimated with averages. 4.3.4 Solution Quality Changes with Weights and Number of Scenarios. Figure 4 provides additional insights by focusing on HH (high in both perishability and stockouts). The discussions are similar in other settings. Subfigure (a) shows that creating 500 scenarios is more than adequate, and after 100 scenarios the improvement in the objective function value is negligible. We also observe that fewer scenarios result in a significant drop in performance for weight ∈ {0.1, 0.5, 0.9}. Therefore, solutions obtained by considering a variety of scenarios perform better. For example, a decision maker who Manuscript submitted to ACM
Weight 0.1 0.5 0.9 e v i tce 100 j b eO 50 v i t scep 0 r e rP 50 e li a teR 100 considers only the latest 3 weeks’ worth of data ( = 3) would be at a significant disadvantage. Subfigure (b) shows the trade-of curve between the user and retailer perspectives with weights ranging from 0 to 1. We observe that increasing the weight from 0 to 0.5 almost triples the user perspective objective while reducing only 0.1 of retailer perspective objective. Therefore, considering both perspectives rather than only one improves the overall quality of the solution. The decision maker can select the best weight according to the needs of the user, retailer, or both.
This article proposes a MIP model and heuristics that consider RS objectives from the user and retailer perspectives. The user perspective aims to obtain highly rated item recommendations while minimizing stockouts. The retailer perspective aims to maximize profit while minimizing the losses incurred by the perished items. Our models find solutions that are high in quality for both criteria. We ofer approximation methods that scale better than the optimization model. We propose a heuristic model and show that its solution quality is nearly as good as the optimal one. Therefore, the reader can decide to aim for the optimal solution and use the optimization model, or use the heuristic, which is faster to solve and more scalable. Finally, we study the improvements made to the objective function values using our models, and compared the solutions with each of the benchmarks in diferent settings.
Our work can be extended in multiple directions. Firstly, more emphasis on inventory could be incorporated into the retailer perspective. In this way, excess inventory could be considered and items with higher storage spaces might need to be recommended more often. In our work, we create recommendations considering inventory as constant (although not deterministic), however, inventory levels of items could be added as decision variables as well. Note that, diferent user segments could behave diferently to stockouts (e.g., purchasing a substitute), and incurring diferent penalties to diferent user segments can be a possible direction.
The stochasticity can be applied to diferent parts with more knowledge of the uncertainties. Scenarios can be generated using the background knowledge of the system. For example, the inventory generation process can represent a problem with supply chain disruptions. Our work assumes the distribution of the parameters, but more work can be done solely focusing on the solution quality changes tied to the distributions. If more complex distributions are considered, the solution quality of the models may change, and it would be worthwhile to investigate the changes in solution quality with changes in distributions.
Manuscript submitted to ACM
While creating our parameters such as the ratings of the items for the users and the efect of recommendation on the increased demand for a given item, we had to make certain assumptions. We use an online retailer dataset in an ofline setting. If our work is extended to an online setting then it would be possible to understand and update our parameters accordingly. Next, by obtaining data from the users continuously, we could improve the quality of the parameters for each user to reflect their needs better. Even in an ofline setting, future research can include diferent parameter creation ideas and investigate the changes in solution qualities in diferent settings.